DIRECTIONS: Each questions is followed by two statements, A and B. Answer each question using the following instructions.
Choose 1: if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.
Choose 2: if the question can be answered by using either statement alone.
Choose 3: if the questions can be answered by using both the statements together, but cannot be answered by using either statement alone.
Choose 4: if the question cannot be answered even by using both the statements together
Questions (Detailed solutions given at the end)
(1) What is the value of the two-digit positive integer N?
A. Four times N is 48 less than the square of the smallest two-digit number.
B. N is a prime number whose square lies between 150 and 250.
(2) ABCD is a cyclic quadrilateral. Is ABCD a rectangle?
A. B || CD.
B. ∠ A + ∠ C = 1800
(3) What is the value of the positive integer n?
A. The product of the numbers a, and b, which are respectively three less and two less than n, is 0.
(4) What is the perimeter of the triangle ABC? One of its side is 10√3 units.
A. ABC is the hypotenuse of the right angle triangle ABC.
B. The sum of the areas of the semicircles described on the three sides of the triangle ABC is 100 π sq. units.
(5) The cost price of an article is 100. Find the profit made by selling it.
A. Ten percent discount was given on the list price and the profit percentage made is 25 percentage points more than the discount percent.
B. List price is Rs.180 and profit percent is 1/5th of the mark-up percentage.
(6) The length of trains of traveling at 90km/hr crosses train B in 32 seconds.
A. Train A traveling at 90 km/hr crosses train B in 32 seconds.
B. Train A and B are not traveling in the opposite directions.
(7) Find the value of the real number N, where N > 0?
A. N is a two digits prime number less than 15, whose square and cube have the digit 1 occurring more than once.
B. N is a composite number less than 10, whose square and cube have their sum of digits equal to the number itself or a multiple of it.
(8) ((10)^n+5)/3 is an integer?
A. n is an integer.
B. n is and natural integer.
(9) Will A and B take more than 14½ days to complete the work working together?
A. If they work on alternate days with A starting the work, they take 28½ days to complete the work.
B. If they work on alternate days with slower person among A and B starting the work, they take 29 days to complete the work.
(10) The length of train A and B are 4000m and 350 respectively. What is the speed of the train B?
A. Train B crosses train A which is traveling at 60km/hr in 22 seconds.
B. The speed of trains B is more than the speed of trains A.
From statement A alone
4n + 48 = 102
4n = 52
A alone is sufficient.
From statement B alone:
Numbers whose squares lie between 150 and 250 are 13, 14 and 15
Among these A, only 13 is a prime number.
:. B alone is sufficient.
Even upon using both the statements we can only conclude that two of the opposite sides are parallel and sum of 2 angles is 180°.
In order to conclude that ABCD is a rectangle which is also a cyclic quadrilateral we also need to know whether the opposite sides are equal in length.
(n - 3) (n - 2) = 0
n = 2 or 3
∴ A alone is not sufficient
Only for n = 2
1! = 1
B alone is sufficient.
Given, sum of areas of semi-circles x, y and z is 100π
If BC = a cm, AC = b cm, AB = c cm.
Area of semi-circle x is π/2 a2/4 cm2
Area of semi-circle y is π/2 c2/4 cm2
Area of semi-circle zx is π/2 b2/4 cm2
½ π/4 (a2 + b2 +c2) =100π
a2 + b2 + c2 = 400
We know that in ΔABC
a2 = b2 +c2 = ∴2 (b2 + c2) = 800
b2 + c2 = 400
b2 + c2 = a2 = 400 ⇒ a = 20
⇒ b or c = 10√3 and ⇒ the sides are 10, 10√3, 20
∴ the perimeter = 30 + 10√3 cm
profit % is 35% (i.e. 10 +25)⇒ profit = Rs.35
From B Mankup% = 80%
⇒ profit % = 1/5 x 80 = 16%
profit = Rs.16
∴ Either statement is sufficient
From A alone.
Tram A takes 30 seconds to cross tram B if it were stationary. Either the trains were moving in the same directions where the speed of train A is greater than the speed of the tram B or the trains are moving in the opposite direction.
If they the trains were moving in the opposite direction, A would have taken less than 30 seconds to cross B.
Therefore, the trains are moving in same direction and the speed of the train
B =90- 750/32 X 18/5
B alone is not sufficient.
From statement A
only 11 is the two digit prime which satisfies the condition.
i.e. (11)^2= 121
(11)^3 = 1331
From statement B
only 9 is such number
when 9^2= 81 and 8 + 1 = 9
9^3 = 729 and 7 + 2 + 9 = 18
n can take negative values for which
(10^n + 5)/3
is not an integer and for positive values of n, 10^n + 5 will result in a number which has the sum of its digits equal to 6 which is a multiple of 3,
∴ (10^n+5)/3 is an integer if n is positive.
From A, n can be negative or positive
From B, n can be only positive and hence (10^n+5)/3 is an integer
From statement A alone,
A worked for 14 ½ days and B worked for 14 days, so they together will be able to finish the work in less than 14½ .
So A alone is sufficient.
From statement B alone,
When the slower person starts the work, the work takes 29 days. So, when the faster person starts the work, the work would be completed in less than 29days.
So, they together need less than 29/2 days to complete the work.
So B alone is sufficient.
From statement A alone, two cases are possible
The two trains are travelling in the same direction. In this case, the speed of train B must be more
than that of train A.
The two trains are travelling in the opposite direction In this case, if speed of train B = 60 km/hr
time taken to cross each other
∴ Speed of train B must be greater than 60 km/hr i.e. greater than speed of train A. Since both the cases are possible, nothing can be concluded. even after using statement B, both cases remain.